Oecologia
DOI 10.1007/s00442-012-2301-4
POPULATION ECOLOGY - ORIGINAL RESEARCH
Comparative demography of an epiphytic lichen: support
for general life history patterns and solutions to common
problems in demographic parameter estimation
Robert K. Shriver • Kerry Cutler • Daniel F. Doak
Received: 9 May 2011 / Accepted: 2 March 2012
Ó Springer-Verlag 2012
Abstract Lichens are major components in many terrestrial ecosystems, yet their population ecology is at best
only poorly understood. Few studies have fully quantified
the life history or demographic patterns of any lichen, with
particularly little attention to epiphytic species. We conducted a 6-year demographic study of Vulpicida pinastri,
an epiphytic foliose lichen, in south-central Alaska. After
testing multiple size-structured functions to describe patterns in each V. pinastri demographic rate, we used the
resulting estimates to construct a stochastic demographic
model for the species. This model development led us to
propose solutions to two general problems in construction
of demographic models for many taxa: how to simply but
accurately characterize highly skewed growth rates, and
how to estimate recruitment rates that are exceptionally
difficult to directly observe. Our results show that
V. pinastri has rapid and variable growth and, for small
individuals, low and variable survival, but that these traits
are coupled with considerable longevity (e.g., [50 years
mean future life span for a 4-cm2 thallus) and little
Communicated by Miguel Franco.
Electronic supplementary material The online version of this
article (doi:10.1007/s00442-012-2301-4) contains supplementary
material, which is available to authorized users.
Present Address:
R. K. Shriver (&)
University Program in Ecology, Duke University,
Durham, NC 27708, USA
e-mail: [email protected]
K. Cutler D. F. Doak
Department of Zoology and Physiology,
University of Wyoming, Laramie, WY 82071, USA
deviation of the stochastic population growth rate from the
deterministic expectation. Comparisons of the demographic patterns we found with those of other lichen studies
suggest that their relatively simple architecture may allow
clearer generalities about growth patterns for lichens than
for other taxa, and that the expected pattern of faster
growth rates for epiphytic species is substantiated.
Keywords Demography Life history Lichens Life span Epiphytes
Introduction
The life history of a species is the combination of traits
regulating population dynamics and also individual fitness.
This set of traits governs both a species’ ability to persist in
a given environment and many aspects of its ecological
dynamics, including population changes, ecosystem role
(e.g., biomass accumulation), and community interactions.
Development of general theories explaining the life history
patterns within and across taxonomic groups has been topic
of longstanding interest in ecology (see e.g., Cole 1954; or
more recently, Linares et al. 2007; Garcia et al. 2008).
Despite this interest, quantitative characterizations of full
life histories have concentrated on vertebrates, vascular
plants, arthropods (van Straalen 1985; Boggs and Ross
1993), and some commercially important mollusks (e.g.,
Chen and Liao 2004), with far less attention to most other
taxonomic groups (but see, for example, Hughes and
Jackson 1985; McFadden 1991; Linares et al. 2007; Rogers
1989). If generalities about life history variations and their
ecological drivers are to be adequately tested and refined, a
considerably broader range of taxa should be subjected to
careful life history analysis, especially those with physiological
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structures and constraints differing from those of the common
focal groups in population ecology.
Lichens are one of the many under-represented groups
in life history studies. Lichens are major members of many
communities worldwide, and have been the subject of
numerous ecological investigations. Major themes in the
ecological literature of lichens include their sensitivity to
pollutants (Conti and Cecchetti 2001), patterns of species
diversity (Dietrich and Scheidegger 1997; Rosentreter
1995), and their important roles in nutrient and energy
flows (Pike 1978; Knops et al. 1996). However, interest in
lichen ecology has not extended to any extensive degree to
their population ecology, including life history analysis.
Survival, growth, and reproductive rates of lichens are the
drivers that shape their community and ecosystem roles,
but of these, only growth patterns have received any substantial attention (Armstrong and Bradwell 2011; but see
Rhoades 1983; Loso and Doak 2006). While many studies
have sought to quantify lichen growth rates, the focus of
most research has either been biomass accumulation or the
use of lichen sizes to date surfaces for geological studies,
rather than on understanding their ecological dynamics per
se (Benedict 2009; Bradwell and Armstrong 2007; but see
Armstrong and Bradwell 2011). Recent work has emphasized the diversity of lichen growth patterns (Armstrong
and Bradwell 2011); however, little attention has been
given to the selective environments that would produce
different life history patterns—in particular for the many
species that, like epiphytes, must cope with dynamic substrates with limited durations. In addition, few attempts
have been made to measure survival or reproduction or to
incorporate multiple rates or temporal variance into a
complete life history analysis.
Here, we apply a demographic approach to quantify the
life history of a common epiphytic lichen, V. pinastri, in
south-central Alaska. V. pinastri is a foliose lichen of
temperate and subarctic forests, and occurs predominantly
on the relatively short-lived trunks of Alnus shrubs
throughout large areas of its range. We used a 6-year
demographic study of V. pinastri to estimate demographic
patterns for this typical epiphytic species. Our analyses
focus on two questions. (1) What are the basic demographic patterns exhibited by V. pinastri, and what life
history characteristics (e.g. lifespan) do these lead to? (2)
Does a comparison of the growth patterns of V. pinastri
with those of other lichens support generalities from life
history, especially generalities about life history variation
in response to habitat stability or disturbance regime? In
particular, we would expect epiphytic species to show
demographic patterns commensurate with their often shortlived substrates. In addition to addressing these issues,
during the course of our work, we confronted two common
problems in the development of many demographic
123
models—the efficient parameterization of multiple modes
of growth and shrinkage, and the inability to directly
observe recruitment events—and suggest general solutions
to these common demographic stumbling blocks.
Materials and methods
Species biology, study sites, and population sampling
Vulpicida pinastri is a circumboreal epiphyte which occurs
across boreal and high-altitude temperate forests of Europe
and North America. V. pinastri has a compact, foliose
growth habitat and most individual thalli can be readily
distinguished. Three reproductive structures are present on
thalli: sexually reproducing apothecia are present but
uncommon; luminant yellow powdery soredia, from which
the species derives its charming common name ‘‘Powdery
Sunshine Lichen,’’ are abundant; and conidia-producing
pycnidia are also present (both soredia and pycnidia are
asexual reproductive structures). We were not able to distinguish between new thalli arising from sexual versus
either mode of asexual reproduction.
All fieldwork was conducted in the Kennicott Valley, in
the Wrangell Mountains of Alaska. Eight study sites were
haphazardly chosen in mature white spruce (Picea glauca)/
alder (Alnus viridis ssp. crispa) forest. All study sites were
located within 0.30 km of one another and between
700–730 m elevation. In this habitat, V. pinastri primarily
occurs on the bark of alders (A. viridis ssp. crispa), with far
smaller numbers on spruce. A spruce bark beetle outbreak
occurred in the study area, peaking in 1996 (Matsuoka and
Handel 2007) with low levels of continuing tree mortality
throughout the study period (D.F.D., personal observation).
Tree death further thinned the already sparse spruce canopy, but had little obvious impact on the already dense
alders in the subcanopy.
In 2004, four study sites were established. At each site,
five alder stems were chosen, and on each, ten lichen thalli
were individually marked with a carpentry staple and aluminum tag and subsequently followed until their death or
the end of the study in 2009. In 2005, four additional sites
were established, for a total of 400 individual lichen thalli.
In each year (ranging from 18 May to 13 June), each thallus
was relocated and digitally photographed with a scale bar.
Thallus surface areas were subsequently estimated using
Adobe Photoshop (Adobe Systems, San Jose, CA, USA).
Individual thalli were distinguished by growth form and
isolation; focal thalli were haphazardly chosen to span the
full distances along each alder stem on which V. pinastri
occurred, and to sample a wide range of thallus sizes.
To quantify establishment of new thalli, we collected
two additional datasets. Two 2 9 15 cm2 recruitment
Oecologia
plots, established on stems near others with focal thalli,
were photographed in each of the eight sites in each year
and compared across years to locate new lichens. Unfortunately, this method resulted in very few clearly identifiable new thalli (four over the entire study). As an
alternative, we made estimates of recruitment based on
predicted population size distributions. For this estimation
procedure, we quantified the size distributions of the entire
lichen populations on six alder stems collected near our
study sites in 2010 (total of 653 thalli). On each stem, we
measured the major and minor axes of all lichens occurring
from *0 to 200 cm up the stem (the range of heights of
nearly all lichens in our study area) and visually estimated
the percentage of the elliptical outline of each thallus that
was not filled. Measured thalli were assumed to approximate an ellipse and visual estimates of unfilled ellipse area
were used to correct deviations from this ideal shape.
These visual estimates of thallus area correspond well with
those from our digital analysis (r2 = 0.947, n = 20 thalli:
slope not significantly different from 1).
Estimation of vital rates
We characterized the demography of V. pinastri using
continuous, size-dependent functions for growth, variance
in growth, and survival (Easterling et al. 2000; Morris and
Doak 2002). For each vital rate, we fit a series of 8–12
alternative general linear models (GLMs; see ESM), and
used AIC comparisons to identify the best-supported model
(cf. Doak and Morris 2010; Palmer et al. 2010), including
effects of size, year (categorical), and their interactions.
Initial graphical exploration of the data indicated that
growth was far more linear when using (thallus area)0.5 and
we thus used the square-root of area as the basic size
measure in all GLM analyses. This pattern corresponds to
findings suggesting that only the part of a lichen thallus near
the periphery can contribute to radial growth (Armstrong
and Smith 1998; Aplin and Hill 1979).
Modeling of V. pinastri growth was complicated by a
problem that plagues many other demographic studies of
plants and some animals: while most individuals grow or
shrink by modest amounts and are well-approximated by
normally distributed errors around an average growth rate
(Easterling et al. 2000), a smaller number suffer much
more extreme shrinkage (Wikelski and Thom 2000;
Salguero-Gomez and Casper 2010) resulting in a highly
skewed distribution of growth rates (Fig. 1a, b). In our
system, such shrinkage is most often due to mechanical
damage to thalli from mammals or falling branches. To
account for these two types of growth without adding
undue complexity to our models, we estimated growth and
shrinkage as a two-part process. First, each thallus has a
size- and year-dependent probability, pn, of undergoing
‘normal growth or shrinkage’ (NGS) and a (1 - pn)
probability of undergoing ‘extreme shrinkage’ (ES). The
probabilities of reaching any given size if undergoing NGS
or ES are then characterized by their own size- and yeardependent means and variances.
While the use of a two-part growth process is straightforward, it requires a clear and justifiable method of classifying
each observed annual growth rate as NGS or ES. Our goal in
making this distinction is to separate normally distributed
growth and shrinkage rates from more extreme amounts of
shrinkage. While this is simple in concept, there was not a
sharp break between these two sets of growth rates in our data
(Fig. 1a). Therefore, we used the following approach: (1)
0.5
finding the difference between (area)0.5
t and (area)t?1 for all
thalli across all years and taking the mean of these values
(0.00947) as the average growth rate (while there is a statistically significant effect of starting size on these values, it is
extremely weak: r2 = 0.02811, p \ 0.05), (2) estimating the
average squared deviations (variance) around this mean
using only the positive differences, (3) using this estimate
of the mean and variance of growth differences to find
the lower 1 % tail of the corresponding normal cumulative distribution function (CDF) for size differences
(-0.26676), and (4) using this lower value to make the
cutoff between NGS and ES values. This results in a normally distributed set of NGS values and a skewed set of
much rarer ES events (Fig. 1b). We followed Easterling
et al. (2000) in assuming normally distributed errors for the
mean and variance of NGS, using (area)0.5
t?1 as our dependent variable and (area)0.5
,
area
,
and
year
as potential
t
t
explanatory variables. For analyses of mean ES, the ratio of
0.5
(area)0.5
was used as the dependent variable to
t?1/(area)t
better achieve normality. Thus, we fit alternative models
for five growth processes: the probability of NGS, the mean
and variance of NGS, and the mean and variance of ES.
Modeling of survival and pn used logistic models, while
all other growth rates were modeled assuming normally
distributed errors. Estimation of recruitment rates was
based on predictions from full matrix models and is
described below.
Model construction and analysis
Separate projection matrices were constructed for each of the
five annual transitions, with year-specific effects on vital
rates when supported by AIC analysis (ESM Table S2). We
used a relatively fine division of sizes: 25 classes of 0–2.5 cm
in 0.1-cm intervals (where size classes defined as area1/2).
This precision approaches that of most implementations of
integral projection models, while retaining the advantages of
a matrix model formulation in implementation and interpretation. All the aji matrix elements below the top row (the
reproductive elements) were estimated as:
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b
2.5
Normal growth
Extreme shrinkage
400
2.0
Number of lichens
Thallus area in year t+1 (cm)
a
1.5
1.0
0.5
0.0
0.5
1.0
1.5
2.0
−1.5
−1.0
−0.5
0.0
0.5
1.0
Difference in thallus area from year t to t+1 (cm)
d
6
0.35
Pred. size dist.
Obs. size dist.
0.30
Proportion of population
5
−Log likelihood
100
2.5
Thallus area in year t (cm)
4
3
2
1
0
0.25
0.20
0.15
0.10
0.05
0.00
0.0
0.1
0.2
0.3
0.4
Recruits/ periphery (cm)
Fig. 1 Fitting of growth and reproductive rates. a Plot of (Areat?1)1/2
versus (Areat)1/2, showing skewed distribution of growth. b Histograms of normal growth and shrinkage (blue) and extreme shrinkage
(red) values. c Likelihood profile for estimates of recruitment rate
aji ¼ si pn;i nji þ 1 pn;i mji
where si is the probability of survival for the ith size
class, pn,i is the probability of ‘‘normal growth or
shrinkage’’ for the ith class, nji is the probability of normally growing or shrinking from the ith class to the jth
class, and mji is the probability of moving from the ith to
the jth class with extreme shrinkage. To estimate nji and
mji values, we used the mid-point size for class i as the
starting size, and a normal CDF to calculate the total
probability of falling within the range of sizes in the jth
class.
Reproductive elements, a1i, could not be directly estimated from our data, but could be estimated based on
predictions of a full demographic model. By assuming that
the relative reproductive contribution of each size class was
proportional to thallus circumference (see ESM for discussion of this assumption and alternatives), we reduced
the estimation of reproduction to a single, size-relative
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200
0
0.0
c
300
0.0
0.5
1.0
1.5
2.0
2.5
Thallus area (cm)
using predictions of population stage structure (horizontal dashed line
boundaries of 95 % confidence limits). d Observed and predicted size
distributions from fitting r, the reproductive rate
parameter, r. We used an optimization routine to find the
values of r resulting in mean matrices that best predicted
either k = 1 or the observed size structure of the population (see ESM). The estimated r values from these two
methods were then inserted into each year-specific matrix,
providing a fully-parameterized stochastic model for V.
pinastri. We used the resulting model to compute longterm stochastic growth rate (kS) values, using independent
identically distributed (IID) selections of our five annual
matrices (10,000 years of growth, discarding the first
1,000 years), and to generate age distributions for thalli of
different sizes, as well as the mean total life span conditional on reaching a given size, using the average matrix
(Cochran and Ellner 1992). To estimate confidence limits
around the kS value, we employed a parametric bootstrap
procedure based on the means and covariances of parameter estimates for the best predictive model for each vital
rate and using a value for r, the reproductive rate, derived
from the best fit model.
Oecologia
Comparative life histories of lichens
To compare our findings with those for other species, we
assembled literature data on lichen demographic rates and
life history patterns. First, we searched Web of Knowledge
and Google Scholar for ‘‘lichen’’ and ‘‘demography’’,
‘‘population’’, ‘‘population model’’, ‘‘growth rate’’, ‘‘survival’’, ‘‘mortality’’ or ‘‘dispersal,’’ and found 85 relevant
studies. While few studies report survival or recruitment
rates (ESM Appendix S1), we found 13 datasets with sizedependent growth rates that we could compare to those for
V. pinastri. As all these results were presented graphically,
we used the image-capture software Data Thief (Tummers
2006) to estimate the data values for our analyses. Lichen
growth rates were reported in a number of different ways and
we converted all of these to a relative growth rate (Woolhouse 1968): RGR = log(A2) - log(A1)/t2 - t1, where A1
and A2 are the thallus surface areas at times 1 and 2,
respectively, and t1 and t2 are the dates of the measurements,
in years. If lichen areas were not reported, we estimated them
from the diameters or radii, assuming that the thalli were
approximately circular. We used a loess fitting function
(‘‘loess’’ in R; R development core team 2011), with a span of
1.5 to create smoothed curves that reasonably described the
size–growth relationship for each species and growth for all
years in our V. pinastri study. We used only the positive
growth rates for all species to estimate a size-specific growth
curve, omitting individuals that shrank from this analysis.
The lichen studies found ranged from tropical to boreal
environments and from arid to mesic habitats. To compare
growth rates while controlling for habitat effects, we used the
estimated maximum relative growth rate (MRGR) of juvenile lichens for each study shown in Fig. 4, including three
separate studies for Rhizocarpon geographicum as well as
two additional estimates for Porina epiphylla (MRGR 1.57)
and Strigula subtilissima (MRGR 3.57) (Rogers 1989).
Because there could be an effect of smallest size of lichen
measured, we estimated the minimum relative growth rate
for all species at the relatively small radius of 0.5 cm.
We regressed log(MRGR) on average annual temperature
and precipitation from WorldClim (v.1.4, http://www.
worldclim.org; explained in detail by Hijmans et al. 2005),
as well as substrate as a categorical variable (see ESM for
detail on models tested for MRGR prediction).
reflecting considerable variation over the five transition
periods (Fig. 2; see ESM for model fitting results). The
probability of NGS ranged from [95 % in the 2007–2008
transition to \70 % in 2006–2007. Survival rates of small,
but not large, thalli showed similarly high variation
(Fig. 2b). Variation in the probability of normal growth
and the mean of normal growth is highly correlated
(Pearson’s r = 0.82 for a 1.5-cm thallus), but neither rate
covaries substantially with survival rate (r = -0.076 and
0.057 for s of 0.25-cm thallus with pn and mean NGS,
respectively). The best models for mean ES and variance of
both growth rates show substantial variation with size
(Fig. 2d; ESM Fig. S1) but no inter-annual variation.
Estimating r, the recruitment rate, by fitting to a stable
population growth rate or by matching the observed size
distribution gave broadly comparable estimates. To achieve
a mean matrix with k = 1, r = 0.047 recruits per cm of
thallus periphery, while fitting to the observed stage structure
yielded a maximum likelihood estimate of r = 0.185, with
a relatively narrow likelihood profile (Fig. 1c). A mean
matrix including this latter value predicts a stable stage
distribution (SSD) that closely matches that observed in
2010 (Fig. 1d). Using r from the k = 1 criteria produced
an estimate of stochastic growth, ks, of 1.003, while the
SSD r gave a mean matrix k = 1.036 and ks = 1.037
(1.0052–1.0621 95 % CI).
To visualize the life history patterns implied by the
demographic parameters, we first ran stochastic simulations to estimate survival curves, as well as estimating
survival from the mean matrix (Fig. 3a). The results indicate that, while population growth and individual performance are variable from year to year, V. pinastri thalli
nonetheless have potentially long life spans, with a new
thallus having a 10.3 % probability of reaching 20 years of
age, and a 4.8 % probability of achieving 50 years. This
longevity is reinforced by patterns in conditional total life
span and mean age at residence for different size classes
(Fig. 3b, c). For example, a thallus of 0.20 cm2, a moderately small size, is predicted to be on average 27 years old
and has a conditional total average lifespan of 46 years.
Note that these predictions do not account for mortality due
to substrate death (thalli rapidly die once the alder stem
on which they reside has died; D.F.D., personal observation), and thus are likely to overestimate the mean and
variance of size-specific lichen ages, especially for larger
individuals.
Results
Comparative life histories of lichens
Vulpicida pinastri demography
The best predictive models for the probability of normal
growth, mean normal growth, and survival all include
effects of year and interactions between size and year,
We were able to find only a handful of previous studies that
attempted to estimate either recruitment or survival in ways
comparable to a standard demographic study (see ESM).
For survival, only two studies contained directly
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Probability of growing normally
a
1.0
0.9
0.8
b
1.00
Probability of surviving
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0.95
0.90
0.85
Year
04−05
05−06
06−07
07−08
08−09
0.80
0.7
0.75
d
0.25
Mean extreme shrinkage rate(cm)
Mean normal growth rate(cm)
c
( λ)
(1.12)
(1.11)
(0.98)
(0.99)
(1.05)
0.20
0.15
0.10
0.05
0.00
−0.05
0.5
1.0
1.5
2.0
2.5
Thallus area (cm)
−0.5
−1.0
−1.5
0.5
1.0
1.5
2.0
2.5
Thallus area (cm)
Fig. 2 Size-dependent vital rate functions. Plots show best-fit
predictions of the a probability of normal growth, b the probability
of survival, c mean normal growth, d and mean extreme shrinkage.
Year-specific predictions are shown for rates with year effects in the
best-supported models. The legend shows year-specific population
growth rates
comparable rates. Golm et al. (1993) found decreasing
survival rates with increasing lichen size, the opposite of
our findings for V. pinastri, but this study compares only
two size classes and their definition of mortality is closer to
what we have called extreme shrinkage. Rhoades (1983)
found survival rates ranging from 0.75 to 0.878 for six size
classes of Lobaria oregana (V. pinastri survival varies
from *0.75 to very close to 1) and a Type 3 survivorship
curve similar that of V. pinastri.
Similarly, recruitment is rarely estimated, and especially
not as a per capita rate to which we could compare our
rates. We found 23 attempts to address some aspect of
reproduction, none of which could be compared to our
estimate of successful propagules per unit size. Some of
these studies look at the relationship between size of thallus
and number of apothecia, rather than number of successful
propagules (Ramstad and Hestmark 2001; Jackson et al.
2006). Again, Rhoades (1983) is the most comparable
study, finding 0 lobules released from the smallest size
class lichen up to 162 lobules released from the largest size
class (thalli [5 g) of lichen, but with no estimates of successful establishment of recruits. Propagule deposition can
be measured directly using a sampling method from
Armstrong (1987, 1990). However, Armstrong was not
directly interested in demography, and thus his methodology does not allow estimates of successful propagule
establishment needed for demographic analysis.
Estimates of lichen growth rates are far more common,
with over 22 studies reporting size-dependent growth in
one manner or another, and comparable growth estimates
for 11 species (Fig. 4). Some of these studies were not
amenable to comparison due to use of biomass instead of
area, non-annual growth rates, or other differences in the
format of the presented data, and we did not present all of
the studies done on R. geographicum, which are numerous
due to this species’ common use in lichenometry. In a few
other cases, only one of multiple datasets for a species was
used, and we chose the most complete of these studies. All
the comparable studies found similar patterns, with
declines in relative growth rate with increasing size
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b
1.0
Total conditional lifespan (yr)
Probability of survival
a
0.8
0.6
0.4
0.2
140
120
100
80
60
40
20
0.0
0
10
20
30
40
50
0.0
0.5
Time (yr)
1.0
1.5
2.0
2.5
Thallus area (cm)
c
d
140
1
120
0
100
−1
ln(MRGR)
Age at residence (yr)
Fig. 3 Life history patterns for
V. pinastri and comparisons
with other lichens.
a Survivorship curves for thalli
from 100 stochastic simulations
and for the mean matrix (bold
line). b Total life span,
conditional on reaching a given
size class (labeled with midclass size), predicted with mean
matrix (mean ± SE). c Age of
thalli of a given size, predicted
with mean matrix (mean ± SE).
d Regressions of the log of
maximum relative growth rates
(MRGR) of epiphytic and
saxicolous lichen types with
average annual temperature for
16 studies; two points are
located at (5, -1.8) and three
near (10, -2)
80
60
−2
−3
40
Epiphytes
Rock
−4
20
−5
0.0
0.5
1.0
1.5
2.0
2.5
Thallus area (cm)
towards a constant RGR value, though with variable
absolute rates and slopes. V. pinastri has relatively fast
maximum juvenile growth compared to two arctic species,
R. geographicum (Haworth et al. 1986; Bradwell and
Armstrong 2007; Armstrong 1983) and Alectoria minuscule (Haworth et al. 1986), but slower than Pseudocyphellaria crocata (Larsson and Gauslaa 2011), Buellia
canascens (Aplin and Hill 1979), Lobaria pulmonaria
(Larsson and Gauslaa 2011), Lobaria scrobiculata (Larsson and Gauslaa 2011), Xanthoparmelia cumberlandii
(Golm et al. 1993), Parmelia conspersa (Armstrong 1973),
and Parmelia saxatilis (Armstrong 1973). Lichens with
similar growth rates to V. pinastri are Parmelia glabratula
(Armstrong 1973) and Parmelia oribicular (Armstrong
1973). While the consistent deceleration of growth with
size and the absence of sharp break points in these growth
curves suggest that a fairly general growth rate function
could apply to all foliose and crustose lichens, the broad
annual growth variation we found in our study also cautions against any assumption of stable annual growth rates.
The apparently more stable growth patterns for other species in Fig. 4 is in large part due to small sample sizes or
highly averaged data. In contrast to our 158–344 individual
−15
−10
−5
0
5
10
15
20
Average annual temperature (°C)
estimates of growth per year (1,543 total), the range of
sample sizes we found in the literature was 15–71, with a
mean of 40.6 individual annual growth estimates.
As shown in Fig. 4, epiphytic lichens do not always
have higher growth rates than saxicolous species. However,
the best of the four models of MRGR chosen by AIC,
which includes temperature and precipitation effects (adj.
r2 = 0.9025; see ESM), shows a positive effect on growth
of temperature (p \ 0.001) and faster growth for epiphytic
than for saxicolous species (p \ 0.001) (Fig. 3d).
Discussion
Our parameterization of a full demographic model for
V. pinastri adds to the short list of full life history characterizations for lichens. In part, our results confirm generalities about lichen life histories, with remarkably high
life spans predicted for a species that is both small (maximum thallus area in our study 6.6 cm2) and exists on
a relatively short-lived substrate. Indeed, longevities for
V. pinastri are comparable to that of many long-lived
plants (Linares et al. 2007; Garcia et al. 2008). However,
123
Oecologia
Relative growth rate = ln(A2/A1)
P. saxatilis
B. canascens
X. cumberlandia
P conspersa
L. pulmonaria
L. scrobiculata
P. crocata
P. oribicular
V. pinastri
P. glabratula
R. geographicum
A. minuscula
e
0.8
0.6
s
s
0.4
0.2
s
se
e
s
e
0.0
s
s
s
s
s
0
5
10
15
20
Thallus radius (cm)
Fig. 4 Smoothed relative growth rates for 12 lichen species (14
studies) as a function of thallus radius. A single line is plotted for all
years of our study combined, and further lines for the data from each
other species, except R. geographicum (data sources: Armstrong
1973, 1984; Haworth et al. 1986; Bradwell and Armstrong 2007;
Lättman et al. 2009; Larsson and Gauslaa 2011; Aplin and Hill 1979).
Saxicolous (s) lichens and epiphytic (e) lichens are distinguished near
the maximum relative growth rates of each species
we also find high variance in demographic performance
from year to year, with especially large swings in growth
rates of large thalli and survival of small thalli (Fig. 2).
While comparable data are difficult to find for a representative range of other species, this vital rate variance implies
that individual lichens are not as well-buffered against
environmental factors as might be thought, although survival rates of large individuals, often the most demographically important set of vital rates (Franco and
Silvertown 2004; Heppell et al. 2000), are relatively
invariant (Fig. 2b), conforming to general life history
expectations (Pfister 1998). The relatively simple structure
of lichen thalli may help explain these patterns. Lichens
have no equivalent to an underground storage organ to
buffer growth or survival against ephemerally poor conditions. Given the lack of any protected structures or storage
organs, high variance in growth rates is perhaps unsurprising, even if uninvestigated in past studies. However, the
coupling of high variance in growth with a relatively long
life span is still surprising, given patterns seen in other taxa
(Garcia et al. 2008). At a population level, the wide variance
in annual k values (Fig. 2) shows that V. pinastri has a
relatively labile life history. However, the small differences
between mean and stochastic population growth rate estimates indicate that V. pinastri life history is nonetheless
well buffered against environmental variability.
Comparison of published lichen growth rates and those
of V. pinastris shows a similar pattern of declining relative
123
growth with size for all species (Fig. 4), in line with what
would be expected from peripheral thallus growth (Armstrong and Smith 1998; Aplin and Hill 1979). In general,
this growth pattern conforms with an expectation of
decreasing relative growth rate as individual size increases,
leading to exponential vegetative growth as seen in plants
and many organisms. However, the apparent ubiquity of
this trend is still somewhat surprising given past disputes
over how lichen growth rates change as thallus size
increases (Aplin and Hill 1979; Loso and Doak 2006).
Perhaps more interesting is the relationship between substrate type and growth (Fig. 3d). Consistently higher
growth rates of epiphytic lichens, compared to saxicolous
species in similar climate conditions, suggests that epiphytes may have altered demographic rates that make them
better suited to their relatively short-lived substrate. Epiphytes of all taxa must grow and produce offspring within
the often short, variable life span of their host substrate, in
our case alder stems that rarely live longer than 50 years
(unpublished data). In contrast, saxicolous individuals live
in a comparatively stable and long-lived substrate, potentially allocating resources to thallus thickening and other
structural investments that would be beneficial over a
longer period. Previous work on lichens has demonstrated a
tradeoff between thallus thickness and dispersal (and thus
reproduction) (Johansson et al. 2007), but the degree to
which substrate influences this or other life history patterns
(e.g., longevity) remains unexplored. More generally, our
results for V. pinastri and for the comparative growth rates
of lichens suggests that epiphytes may represent productive
groups with which to test theories of life history evolution
in relation to habitat stability, especially since, unlike many
substrates, the dynamics of the living bodies of plants may
be carefully quantified.
In turning field data into model parameters, we faced
two problems that are common to many demographic
studies. First, we could not directly observe reproduction
and recruitment. The approach of estimating this rate using
population level predictions, and, in particular, the predicted and observed stage structure, is promising for other
studies. Assuming k = 1 is a more common solution to this
issue, but this approach is neither easily tested against data
in most studies, nor does it allow an actual prediction of
population growth rate, as does use of the stage structure
comparison. One limitation of this approach in our study is
the need to assume that measured size distributions represent the stable stage structure, rather than transient stage
structures. This prevented estimation of inter-annual variation in reproductive rates; however, we have no evidence
to suggest strong flushes of recruitment (personal observation, D.F.D.). And while we lacked the foresight to
collect annual size distributions, the relatively stable survival rates for most thalli of V. pinastri suggests there is
Oecologia
limited inter-annual variation. Another problem is that we do
not have any clear way to distinguish between two possible
size-dependency patterns for reproduction (area or perimeterdependence). While for our analyses these two assumptions
give indistinguishable results (see ESM), for analysis of
transient population dynamics following colonization or
disturbance there could be important differences.
The proper quantification of growth probabilities is
similarly an issue for many demographic studies. The use of
continuous state variable functions has increased the efficiency with which growth and shrinkage rates are characterized, but has often relied on assumptions of extremely
simple growth patterns (but see Dahlgren et al. 2011). The
approach we take here is a modest improvement, but one
that greatly increases the realistic characterization of
growth by distinguishing between incremental increases
and decreases in size and what amounts to the severe bad
luck of a minority of thalli. This distinction is likely to exist
for many other plants (Salguero-Gomez and Casper 2010)
and perhaps some animals (Linares et al. 2007).
Overall, our results suggest that lichens may conform to
some life history generalities and confound others. However, the most striking result is that, while lichens are easy
subjects for demographic study, there is striking paucity of
information with which to evaluate their life history patterns. Lichens, tight symbioses between fungi and green
algae and/or cyanobacteria, have very different internal
structure and degrees of integration than do most plants or
animals, and it is not at all clear whether they are likely to
exhibit the same general demographic patterns, given their
potentially low abilities to transport photosynthate or other
materials within thalli (Armstrong 1979; Honegger 1991)
and their multiple modes of sexual and asexual reproduction (Bowler and Rundel 1975). More generally, the vast
majority of demographic studies target a narrow range of
taxonomic groups, with particularly little attention to sessile marine invertebrates (Linares et al. 2007), non-vascular
plants, lichens, or other ecologically dominant groups. This
taxonomic bias in turn hampers efforts to formulate and
test hypotheses regarding general life history patterns.
More encouragingly, our comparison of lichen growth
curves (Fig. 4) hints at more generality concerning growth
rates for lichens than is likely to exist for plants or many
animal taxa, where the complexity of different anatomical
structures may well lead to greater diversity of life history
patterns. As authors have noted for other taxonomic
groups, searching for generalities in life history patterns is
important both for tests of life history theory and as a
practical tool for conservation planning in the face of
limited information (Heppell et al. 2000; Cortés 2002;
Linares et al. 2007). Lichens represent an ecologically
important, species-rich, and taxonomically variable group
for which such comparisons may be particularly powerful.
Acknowledgments This work was supported by NSF DEB 0717049
and 0087078 to D.F. Doak, and by Wyoming NASA Space Grant
Consortium (#NN10AO95H) Fellowships to both K. Cutler and R.K.
Shriver. We thank M. Franco, R. Salguero-Gómez, and one anonymous reviewer for their helpful comments on the manuscript. All
research described complies with the laws of the United States and
Alaska.
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